Two things come to mind. One: If your new grass gets full sun, are you using a full sun seed? If your grass is in shade, are you using a shade-tolerant seed? And if the seeded area gets a mix of both sun and shade, are you using a partial sun/shade grass? Two: Grass, IMO, needs water during the daytime hours when the sun is being demanding. By feeding it at night, the water will permeate through the soil, and by the daytime, when the grass needs water, its already filtered through the soil, thus, stressing the grass especially with the added conditions of the drought. My $.02 says that if you're gonna water, do so it in the morning; not in the evening.
Some other thought(s) ... If the grass is being sun-burnt, then welcome to the club. New grass is more sensitive to the drought, even with watering, than established grass. You can throw down a soil neutralizer in any event (as your own suspicions have been raised) in case the soil is acidic. But I think that if a few months have gone by, the excess nitrogen and such has been neutralized and filtered down through the soil. I could be wrong but that's why it couldn't hurt to neutralize the soil anyway. At the same time, you want to 'feed' the soil so do both. Do the neutralizing first AFTER the ground has been able to hold water from a rain. (It may simply get washed away if you don't time it right because the soil is soooo hard right now.)
One last comment ... If you can get away with throwing down some straw (I don't know how big the area your seeding is) to prevent soil erosion, you'd problably do more good than harm right now. You can plant seed in the fall when it's cooler and the water restrictions are, more than likely, eased. Your neighbors are probably saying all kinds of stuff about you. You may not care but if it can wait 'till Fall, you'd be viewed as helping out during the drought. Right now, it's tough to grow grass even when watering because of the extreme natural conditions outside. When you plant the seed, make sure to get a fertilizer for new grass. Remember, it's new grass you're fertilizing; not established grass.